Rewrite as a simplified fraction. ${0.6\overline{12} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}1000x &= 612.1212...\\ 10x &= 6.1212...\end{aligned}}$ Subtracting the two equations, we have: ${990x = 606}$ ${x = \dfrac{606}{990}} $ ${x = \dfrac{101}{165}} $